Re: fibint(n), fibbinary(n)

On 2026-01-11 23:15, Ruud H.G. van Tol wrote:
> On 2026-01-11 18:18, Bill Allombert wrote:
> > On Sun, Jan 11, 2026 at 05:45:42PM +0100, Ruud H.G. van Tol wrote:
>
> >> I'm looking for an effective (discrete, loop-less) way to derive 
> the n-th
> >> fibbinary number (Zeckendorf representation).
> >> For definitions, see https://oeis.org/A003714.
> >>
> >> [ n | n<-[0..100], !bitand(n,n>>1) ]
> >> [0,
> >> 1,
> >> 2,
> >> 4, 5,
> >> 8, 9, 10,
> >> 16, 17, 18, 20, 21,
> >> 32, 33, 34, 36, 37, 40, 41, 42,
> >> 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85
> >> ]
> [...]

A pretty straight way to generate the sequence as a list:

upto(lim)= {
   my( r=List([0]), t );
   for( i=1, oo
   , (t=r[i]<<1) <= lim || break;
     t && listput(~r, t);
     bitand(t, 2) || listput(~r, t++)
   );
   Vec(r);
}

That does about 1.4M terms per second.

(and it deliberately overshoots by one if lim == 0 (mod 4) is a term)

-- Ruud